Are there textbooks on logic where the references to set theory appear only after the construction of set...
1
In textbooks on logic the authors usually use the notions of set and map immediately, long before the set theory is constructed. That is strange for me, and I want to ask if anybody can advise me a textbook on logic with a "linear structure", without these "circles in definitions"?
EDIT. This question is a reference request, so I hope, if I cross post it to MathOverflow, this will not cause a duplication of efforts for people who plan to post answers. Here is this question at MO.
logic reference-request first-order-logic predicate-logic book-recommendation
edited Dec 29 '18 at 8:37
Martin Sleziak
44.6k8115271
asked Sep 29 '16 at 19:27
Sergei AkbarovSergei Akbarov
837516
|
show 9 more comments
1
In textbooks on logic the authors usually use the notions of set and map immediately, long before the set theory is constructed. That is strange for me, and I want to ask if anybody can advise me a textbook on logic with a "linear structure", without these "circles in definitions"?
EDIT. This question is a reference request, so I hope, if I cross post it to MathOverflow, this will not cause a duplication of efforts for people who plan to post answers. Here is this question at MO.
logic reference-request first-order-logic predicate-logic book-recommendation
edited Dec 29 '18 at 8:37
Martin Sleziak
44.6k8115271
asked Sep 29 '16 at 19:27
Sergei AkbarovSergei Akbarov
837516
Carl Mummert's answer here is quite relevant.
– Henning Makholm
Sep 29 '16 at 19:32
It is not possible in an "absolute" sense: imagine writing a grammar to describe "how language works". Do you think that you can do it without using language in writing the book ?
– Mauro ALLEGRANZA
Sep 29 '16 at 19:35
1
But you can see Kenneth Kunen, The Foundations of Mathematics (2009).
– Mauro ALLEGRANZA
Sep 29 '16 at 19:40
1
@SergeiAkbarov, if you are looking for a treatment of FOL with syntax and not semantics, then you could read the first section of these notes (math.ucsd.edu/~sbuss/ResearchWeb/handbookI/ChapterI.pdf). The semantics stuff comes later and can be skipped. (I am sure there are books too, but I don't have a good source off hand. The one I know of is still being written.)
– Jason Rute
Sep 30 '16 at 16:10
1
For people interested in constructive foundations, here are some relevant links: math.stackexchange.com/a/1808558, math.stackexchange.com/a/1895288. I should note that the question of whether LEM (law of excluded middle) holds is not clear to me beyond the arithmetical hierarchy, even granting the complete collection of the natural numbers, because the original intuition or justification for LEM only applies to assertions about reality (see math.stackexchange.com/a/1888389).
– user21820
Oct 1 '16 at 12:06
|
show 9 more comments
1
1
1
In textbooks on logic the authors usually use the notions of set and map immediately, long before the set theory is constructed. That is strange for me, and I want to ask if anybody can advise me a textbook on logic with a "linear structure", without these "circles in definitions"?
EDIT. This question is a reference request, so I hope, if I cross post it to MathOverflow, this will not cause a duplication of efforts for people who plan to post answers. Here is this question at MO.
logic reference-request first-order-logic predicate-logic book-recommendation
edited Dec 29 '18 at 8:37
Martin Sleziak
44.6k8115271
asked Sep 29 '16 at 19:27
Sergei AkbarovSergei Akbarov
837516
In textbooks on logic the authors usually use the notions of set and map immediately, long before the set theory is constructed. That is strange for me, and I want to ask if anybody can advise me a textbook on logic with a "linear structure", without these "circles in definitions"?
EDIT. This question is a reference request, so I hope, if I cross post it to MathOverflow, this will not cause a duplication of efforts for people who plan to post answers. Here is this question at MO.
logic reference-request first-order-logic predicate-logic book-recommendation
logic reference-request first-order-logic predicate-logic book-recommendation
edited Dec 29 '18 at 8:37
Martin Sleziak
44.6k8115271
asked Sep 29 '16 at 19:27
Sergei AkbarovSergei Akbarov
837516
edited Dec 29 '18 at 8:37
Martin Sleziak
44.6k8115271
asked Sep 29 '16 at 19:27
Sergei AkbarovSergei Akbarov
837516
edited Dec 29 '18 at 8:37
Martin Sleziak
44.6k8115271
edited Dec 29 '18 at 8:37
Martin Sleziak
44.6k8115271
edited Dec 29 '18 at 8:37
Martin Sleziak
44.6k8115271
44.6k8115271
asked Sep 29 '16 at 19:27
Sergei AkbarovSergei Akbarov
837516
asked Sep 29 '16 at 19:27
Sergei AkbarovSergei Akbarov
837516
asked Sep 29 '16 at 19:27
Sergei AkbarovSergei Akbarov
837516
837516
Carl Mummert's answer here is quite relevant.
– Henning Makholm
Sep 29 '16 at 19:32
It is not possible in an "absolute" sense: imagine writing a grammar to describe "how language works". Do you think that you can do it without using language in writing the book ?
– Mauro ALLEGRANZA
Sep 29 '16 at 19:35
1
But you can see Kenneth Kunen, The Foundations of Mathematics (2009).
– Mauro ALLEGRANZA
Sep 29 '16 at 19:40
1
@SergeiAkbarov, if you are looking for a treatment of FOL with syntax and not semantics, then you could read the first section of these notes (math.ucsd.edu/~sbuss/ResearchWeb/handbookI/ChapterI.pdf). The semantics stuff comes later and can be skipped. (I am sure there are books too, but I don't have a good source off hand. The one I know of is still being written.)
– Jason Rute
Sep 30 '16 at 16:10
1
For people interested in constructive foundations, here are some relevant links: math.stackexchange.com/a/1808558, math.stackexchange.com/a/1895288. I should note that the question of whether LEM (law of excluded middle) holds is not clear to me beyond the arithmetical hierarchy, even granting the complete collection of the natural numbers, because the original intuition or justification for LEM only applies to assertions about reality (see math.stackexchange.com/a/1888389).
– user21820
Oct 1 '16 at 12:06
|
show 9 more comments
Carl Mummert's answer here is quite relevant.
– Henning Makholm
Sep 29 '16 at 19:32
It is not possible in an "absolute" sense: imagine writing a grammar to describe "how language works". Do you think that you can do it without using language in writing the book ?
– Mauro ALLEGRANZA
Sep 29 '16 at 19:35
1
But you can see Kenneth Kunen, The Foundations of Mathematics (2009).
– Mauro ALLEGRANZA
Sep 29 '16 at 19:40
1
@SergeiAkbarov, if you are looking for a treatment of FOL with syntax and not semantics, then you could read the first section of these notes (math.ucsd.edu/~sbuss/ResearchWeb/handbookI/ChapterI.pdf). The semantics stuff comes later and can be skipped. (I am sure there are books too, but I don't have a good source off hand. The one I know of is still being written.)
– Jason Rute
Sep 30 '16 at 16:10
1
For people interested in constructive foundations, here are some relevant links: math.stackexchange.com/a/1808558, math.stackexchange.com/a/1895288. I should note that the question of whether LEM (law of excluded middle) holds is not clear to me beyond the arithmetical hierarchy, even granting the complete collection of the natural numbers, because the original intuition or justification for LEM only applies to assertions about reality (see math.stackexchange.com/a/1888389).
– user21820
Oct 1 '16 at 12:06
Carl Mummert's answer here is quite relevant.
– Henning Makholm
Sep 29 '16 at 19:32
Carl Mummert's answer here is quite relevant.
– Henning Makholm
Sep 29 '16 at 19:32
It is not possible in an "absolute" sense: imagine writing a grammar to describe "how language works". Do you think that you can do it without using language in writing the book ?
– Mauro ALLEGRANZA
Sep 29 '16 at 19:35
It is not possible in an "absolute" sense: imagine writing a grammar to describe "how language works". Do you think that you can do it without using language in writing the book ?
– Mauro ALLEGRANZA
Sep 29 '16 at 19:35
1
1
But you can see Kenneth Kunen, The Foundations of Mathematics (2009).
– Mauro ALLEGRANZA
Sep 29 '16 at 19:40
But you can see Kenneth Kunen, The Foundations of Mathematics (2009).
– Mauro ALLEGRANZA
Sep 29 '16 at 19:40
1
1
@SergeiAkbarov, if you are looking for a treatment of FOL with syntax and not semantics, then you could read the first section of these notes (math.ucsd.edu/~sbuss/ResearchWeb/handbookI/ChapterI.pdf). The semantics stuff comes later and can be skipped. (I am sure there are books too, but I don't have a good source off hand. The one I know of is still being written.)
– Jason Rute
Sep 30 '16 at 16:10
@SergeiAkbarov, if you are looking for a treatment of FOL with syntax and not semantics, then you could read the first section of these notes (math.ucsd.edu/~sbuss/ResearchWeb/handbookI/ChapterI.pdf). The semantics stuff comes later and can be skipped. (I am sure there are books too, but I don't have a good source off hand. The one I know of is still being written.)
– Jason Rute
Sep 30 '16 at 16:10
1
1
For people interested in constructive foundations, here are some relevant links: math.stackexchange.com/a/1808558, math.stackexchange.com/a/1895288. I should note that the question of whether LEM (law of excluded middle) holds is not clear to me beyond the arithmetical hierarchy, even granting the complete collection of the natural numbers, because the original intuition or justification for LEM only applies to assertions about reality (see math.stackexchange.com/a/1888389).
– user21820
Oct 1 '16 at 12:06
For people interested in constructive foundations, here are some relevant links: math.stackexchange.com/a/1808558, math.stackexchange.com/a/1895288. I should note that the question of whether LEM (law of excluded middle) holds is not clear to me beyond the arithmetical hierarchy, even granting the complete collection of the natural numbers, because the original intuition or justification for LEM only applies to assertions about reality (see math.stackexchange.com/a/1888389).
– user21820
Oct 1 '16 at 12:06
|
show 9 more comments
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Carl Mummert's answer here is quite relevant.
– Henning Makholm
Sep 29 '16 at 19:32
It is not possible in an "absolute" sense: imagine writing a grammar to describe "how language works". Do you think that you can do it without using language in writing the book ?
– Mauro ALLEGRANZA
Sep 29 '16 at 19:35
1
But you can see Kenneth Kunen, The Foundations of Mathematics (2009).
– Mauro ALLEGRANZA
Sep 29 '16 at 19:40
1
@SergeiAkbarov, if you are looking for a treatment of FOL with syntax and not semantics, then you could read the first section of these notes (math.ucsd.edu/~sbuss/ResearchWeb/handbookI/ChapterI.pdf). The semantics stuff comes later and can be skipped. (I am sure there are books too, but I don't have a good source off hand. The one I know of is still being written.)
– Jason Rute
Sep 30 '16 at 16:10
1
For people interested in constructive foundations, here are some relevant links: math.stackexchange.com/a/1808558, math.stackexchange.com/a/1895288. I should note that the question of whether LEM (law of excluded middle) holds is not clear to me beyond the arithmetical hierarchy, even granting the complete collection of the natural numbers, because the original intuition or justification for LEM only applies to assertions about reality (see math.stackexchange.com/a/1888389).
– user21820
Oct 1 '16 at 12:06